Tutorial : Fortran

1. Tutorial : Fortran By Gopika Sood

2. What is fortran ??? • Fortran is a general purpose programming language, mainly intended for mathematical computations in e.g. engineering. • Fortran is an acronym for FORmula TRANslation, and was originally capitalized as FORTRAN • Fortran was the first ever high-level programming languages. The work on Fortran started in the 1950's at IBM and there have been many versions since. By convention, a Fortran version is denoted by the last two digits of the year the standard was proposed Fortran66 Fortran77 Fortran90

3. Why learn fortran ??? • Fortran is the dominant programming language used in engineering applications. It is therefore important for engineering graduates to be able to read and modify Fortran code. • Fortran is the most enduring computer programming language in history. One of the main reasons Fortran has survived and will survive is software inertia. Once a company has spent many man-years and perhaps millions of dollars on a software product, it is unlikely to try to translate the software to a different language. Reliable software translation is a very difficult task. • A major advantage Fortran has is that it is standardized by ANSI and ISO (see footnotes). Consequently, if your program is written in ANSI Fortran 77 then it will run on any computer that has a Fortran 77 compiler. Thus, Fortran programs are portable across machine platforms. • In High Energy Physics, in the scientific community, all the simulations are still done using fortran inspite of the existence of C, C++.

4. Fortran77 Basics : • A Fortran program is just a sequence of lines of text. The text has to follow a certain syntax to be a valid Fortran program. We start by looking at a simple example: program circle real r, area c c This program reads a real number r and prints c the area of a circle with radius r. write (*,*) 'Give radius r:‘ read (*,*) r area = 3.14159*r*r write (*,*) 'Area = ', area stop end The lines that begin with with a "c" are comments

5. Program Organisation • A Fortran program generally consists of a main program (or driver) and possibly several subprograms (or procedures or subroutines). For now we will assume all the statements are in the main program; subprograms will be treated later. The structure of a main program is: program name declarations statements stop end

6. Column position rules : Fortran 77 is not a free-format language, but has a very strict set of rules for how the source code should be formatted. The most important rules are the column position rules: • Col. 1 : Blank, or a "c" or "*" for comments • Col. 2-5 : Statement label (optional) • Col. 6 : Continuation of previous line (optional) • Col. 7-72 : Statements

7. Variables,Types and Declarations Variable Names Variable names in Fortran consist of any letters from a-z or digits 0-9 Fortran 77 does not distinguish between upper and lower case Types and declarations The most common declarations are: integer list of variables real list of variables double precision list of variables complex list of variables logical list of variables character list of variables

8. Expression and Assignment Constants: The simplest form of an expression is a constant. integer constants : 1, 0,-100,32767,+15 real constants: 1.0, -0.25, 2.0E6, 3.333E-1 double precision :2.0D-1, 1D99 complex constants : (2, -3) (1., 9.9E-1) logical constants :.TRUE. .FALSE. character constants : 'ABC' ‘Hello' Expressions The simplest expressions are of the form operand operator operand and an example is x + y

9. Expression and Assignment contd… The precedence of arithmetic operators in Fortran 77 are (from highest to lowest): ** {exponentiation} *,/ {multiplication, division} +,- {addition, subtraction} All these operators are calculated left-to-right, except the exponentiation operator **, which has right-to-left precedence. The above operators are all binary operators. there is also the unary operator - for negation, which takes precedence over the others. Hence an expression like -x+y means what you would expect. Extreme caution must be taken when using the division operator, which has a quite different meaning for integers and reals. If the operands are both integers, an integer division is performed, otherwise a real arithmetic division is performed. For example, 3/2 equals 1, while 3./2. equals 1.5. Assignment The assignment has the form variable_name = expression The interpretation is as follows: Evaluate the right hand side and assign the resulting value to the variable on the left.

10. Logical Expressions Logical expressions can only have the value .TRUE. or .FALSE.. A logical expression can be formed by comparing arithmetic expressions using the following relational operators: • .LT. meaning < (less than) • .LE. <= (less than or equal to) • .GT. > (greater than) • .GE. >= (greater than or equal to) • .EQ. = (equal to) • .NE. /= (not equal to) Logical expressions can be combined by the logical operators .AND. .OR. .NOT.

11. The if statement An important part of any programming language are the conditional statements. The most common such statement in Fortran is the ifstatement, which actually has several forms. The simplest one is the logical if statement: if (logical expression) executable statement If more than one statement should be executed inside the if, then the following syntax should be used: if (logical expression) then statements endif The most general form of the if statement has the following form: if (logical expression) then statements elseif (logical expression) then statements : else Statements endif

12. Nested if statements if statements can be nested in several levels. if (x .GT. 0) then if (x .GE. y) then write(*,*) 'x is positive and x >= y' else write(*,*) 'x is positive but x < y' endif elseif (x .LT. 0) then write(*,*) 'x is negative' else write(*,*) 'x is zero' endif

13. Loops For repeated execution of similar things, loops are used. do-loops The do-loop is used for simple counting. Here is a simple example that prints the cumulative sums of the integers from through n (assume n has been assigned a value elsewhere): integer i, n, sum sum = 0 do 10 i = 1, n sum = sum + i write(*,*) 'i =', i write(*,*) 'sum =', sum 10 continue The general form of the do loop is as follows: do label var = expr1, expr2, expr3 statements label continue

14. While loops do while (logical expr) statements enddo label if (logical expr) then statements goto label endif

15. Arrays Many scientific computations use vectors and matrices. The data type Fortran uses for representing such objects is the array. A one-dimensional array corresponds to a vector, while a two-dimensional array corresponds to a matrix. The simplest array is the one-dimensional array, which is just a linear sequence of elements stored consecutively in memory. For example, the declaration real a(20) declares a as a real array of length 20. That is, a consists of 20 real numbers stored contiguously in memory. By convention, Fortran arrays are indexed from 1 and up. Thus the first number in the array is denoted by a(1) and the last by a(20) Matrices are very important in linear algebra. Matrices are usually represented by two-dimensional arrays. For example, the declaration real A(3,5) defines a two-dimensional array of 3*5=15 real numbers. It is useful to think of the first index as the row index, and the second as the column index. Hence we get the graphical picture: (1,1) (1,2) (1,3) (1,4) (1,5) (2,1) (2,2) (2,3) (2,4) (2,5) (3,1) (3,2) (3,3) (3,4) (3,5)

16. Multidimensional Array Fortran 77 allows arrays of up to seven dimensions.The syntax and storage format are analogous to the two-dimensional case, so we will not spend time on this. The dimension statement There is an alternate way to declare arrays in Fortran 77. The statements real A, x dimension x(50) dimension A(10,20) are equivalent to real A(10,20), x(50) This dimension statement is considered old-fashioned style today.

17. Subprograms When a programs is more than a few hundred lines long, it gets hard to follow. Fortran codes that solve real engineering problems often have tens of thousands of lines. The only way to handle such big codes, is to use a modular approach and split the program into many separate smaller units called subprograms. A subprogram is a (small) piece of code that solves a well defined subproblem. In a large program, one often has to solve the same subproblems with many different data. Instead of replicating code, these tasks should be solved by subprograms . The same subprogram can be invoked many times with different input data. Fortran has two different types of subprograms, called functions subroutines.

18. Functions Fortran functions are quite similar to mathematical functions: They both take a set of input arguments (parameters) and return a value of some type. In the preceding discussion we talked about user defined subprograms. Fortran 77 also has some built-in functions. abs absolute value min minimum value max maximum value sqrt square root sin sine cos cosine tan tangent atan arctangent exp exponential (natural) log logarithm (natural)

19. Functions contd… The structure of a function closely resembles that of the main program. The main differences are: • Functions have a type. This type must also be declared in the calling program. • The return value should be stored in a variable with the same name as the function. • Functions are terminated by the return statement instead of stop. To sum up, the general syntax of a Fortran 77 function is: type function name (list-of-variables) declarations statements return end

20. Subroutine A Fortran function can essentially only return one value. Often we want to return two or more values (or sometimes none!). For this purpose we use the subroutine construct. The syntax is as follows: subroutine name (list-of-arguments) declarations statements Return end Note that subroutines have no type and consequently should not (cannot) be declared in the calling program unit.

21. Simple I/O An important part of any computer program is to handle input and output. In our examples so far, we have already used the two most common Fortran constructs for this: read and write. Read and write Read is used for input, while write is used for output. A simple form is read (unit no, format no) list-of-variables write(unit no, format no) list-of-variables The unit number can refer to either standard input, standard output, or a file. This will be described in later section. The format number refers to a label for a format statement, which will be described shortly. It is possible to simplify these statements further by using asterisks (*) for some arguments, like we have done in all our examples so far. This is sometimes called list directed read/write. read (*,*) list-of-variables write(*,*) list-of-variables The first statement will read values from the standard input and assign the values to the variables in the variable list, while the second one writes to the standard output.

22. Format statements Syntax write(*, label) list-of-variables label format format-code A simple example demonstrates how this works. Say you have an integer variable you want to print in a field 4 characters wide and a real number you want to print in fixed point notation with 3 decimal places. write(*, 900) i, x 900 format (I4,F8.3) The format label 900 is chosen somewhat arbitrarily, but it is common practice to number format statements with higher numbers than the control flow labels. After the keyword format follows the format codes enclosed in parenthesis. The code I4 stands for an integer with width four, while F8.3 means that the number should be printed using fixed point notation with field width 8 and 3 decimal places. The format statement may be located anywhere within the program unit. There are two programming styles: Either the form,at statement follows directly after the read/write statement, or all the format statements are grouped together at the end of the (sub-)program.

23. File I/O It is also possible to read or write from files which are stored on some external storage device, typically a disk (hard disk, floppy) or a tape. In Fortran each file is associated with a unit number, an integer between 1 and 99. Opening and closing a file Before you can use a file you have to open it. The command is open (list-of-specifiers) where the most common specifiers are: [UNIT=] u IOSTAT= ios ERR= err FILE= fname STATUS= sta ACCESS= acc FORM= frm RECL= rl

24. The unit number u is a number in the range 9-99 that denotes this file (the programmer may chose any number but he/she has to make sure it is unique). ios is the I/O status identifier and should be an integer variable. Upon return, ios is zero if the stement was successful and returns a non-zero value otherwise. err is a label which the program will jump to if there is an error. fname is a character string denoting the file name. sta is a character string that has to be either NEW, OLD or SCRATCH. It shows the prior status of the file. A scrath file is a file that is created and deleted when the file is closed (or the program ends). acc must be either SEQUENTIAL or DIRECT. The default is SEQUENTIAL. frm must be either FORMATTED or UNFORMATTED. The default is UNFORMATTED. rl specifies the length of each record in a direct-acccess file.

25. Read and Write revisited The only necessary change from our previous simplified read/write statements, is that the unit number must be specified. But frequently one wants to add more specifiers. Here is how: read ([UNIT=]u, [FMT=]fmt, IOSTAT=ios, ERR=err, END=s) write([UNIT=]u, [FMT=]fmt, IOSTAT=ios, ERR=err, END=s) where most of the specifiers have been described above. The END=s specifier defines which statement label the program jumps to if it reaches end-of-file.

26. Common Blocks Fortran 77 has no global variables, i.e. variables that are shared among several program units (subroutines). The only way to pass information between subroutines we have seen so far, is to use the subroutine parameter list. Sometimes this is inconvenient, e.g. when many subroutines share a large set of parameters. In such cases one can use a common block. This is a way to specify that certain variables should be shared among certain subroutines. Syntax common / name / list-of-variables You should know that The common statement should appear together with the variable declarations, before the executable statements. Different common blocks must have different names (just like variables). A variable can belong to more than one common block. The variables in a common block do not need to have the same names each place they occur (although it is a good idea to do so), but they must be listed in the same order and have the same type.

27. The data statement The data statement is another way to input data that are known at the time when the program is written. It is similar to the assignment statement. The syntax is: data list-of-variables/ list-of-values/, ... where the three dots means that this pattern can be repeated. Here is an example: data m/10/, n/20/, x/2.5/, y/2.5/ We could also have written this data m,n/10,20/, x,y/2*2.5/ We could have accomplished the same thing by the assignments m = 10 n = 20 x = 2.5 y = 2.5

28. Fortran Programming Stlyes There are many different programming styles, but we will try to give some general guidelines that are fairly non-controversial. Portability To ensure portability, use only standard Fortran 77. The only exception we have allowed in this tutorial is to use lower case letters today. Program structure The overall program structure should be modular. Each subprogram should solve a well-defined task. Many people prefer to write each subprogram in a separate file .Comments Let us repeat this: Write legible code, but also add comments in the source explaining what is happening! It is especially important to have a good header for each subprogram that explains each input/output argument and what the subprogram does. Indentation Always use proper indentation for loops and if blocks as demonstrated in this tutorial. Variables Always declare all variables. Implicit type declaration is bad! Try to stick to maximum 6 characters for variable names, or at the very least make sure the 6 first characters are unique.

29. Programming Style contd… Subprograms Never let functions have "side effects", i.e. do not change the value of the input parameters. Use subroutines in such cases. In the declarations, separate parameters, common blocks, and local variables. Minimize the use of common blocks. Goto Minimize the use of goto. Unfortunately it is necessary to use goto in some loops since while is not standard Fortran. Arrays In many cases it is best to declare all large arrays in the main program and then pass them as arguments to the various subroutines. This way all the space allocation is done in one place.

30. Some common errors Here are some common errors to watch out for: Make sure your lines end at column 72. The rest will be ignored! Do your parameter lists in the calling and the called program match? Do your common blocks match? Have you done integer division when you wanted real division?